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RESEARCH PAPERS: Electronic Cooling

Identification of Unknown Heating Elements Embedded in a Rectangular Package

[+] Author and Article Information
Chin-Hsiang Cheng1

Department of Mechanical Engineering, Tatung University, 40 Chungshan N. Road, Sec. 3, Taipei, Taiwan 10451, R.O.C.cheng@ttu.edu.tw

Mei-Hsia Chang

Department of Mechanical Engineering, Tatung University, 40 Chungshan N. Road, Sec. 3, Taipei, Taiwan 10451, R.O.C.

1

Corresponding author.

J. Heat Transfer 127(8), 918-930 (Mar 15, 2005) (13 pages) doi:10.1115/1.1929782 History: Received November 20, 2003; Revised March 15, 2005

The aim of this study is to present a novel inverse heat transfer method, which incorporates an automatic-filter scheme with the conjugate gradient method, for identifying shapes and temperatures of heating elements embedded in a rectangular package. In this report, shapes of the heating elements are visualized by using node-matrix images. A group of unknown heating elements with different shapes, positions, and temperatures are nondestructively identified simply based on the data of the upper surface temperature of the rectangular package. Effects of temperature measurement uncertainty, grid size, and number of measurement points on the top surface on the identification accuracy are evaluated. Results show that the geometric and thermal conditions of the embedded heating elements can be predicted precisely by using the present approach. The approach is found to be stable and insensitive to the temperature measurement uncertainty, and, without overwhelming mathematical manipulation, the form of objective function becomes flexible.

Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Physical model for the test cases

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Figure 2

Grid points, temperature measurement points, and image matrix nodes

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Figure 3

Illustration for the variation of pass value f in a series of subprocesses in iteration

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Figure 4

Flowchart of the process for geometry and temperature identification

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Figure 5

Effects of h∕k on the accuracy of geometry and temperature identification at σ=0 and m×m=21×21. The exact heating element temperature TH,ex is fixed at 110.00 °C.

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Figure 6

Geometry and temperature identification for different numbers of heating elements. Multiples heating elements embedded in a package have equal exact temperatures. The cases at h∕k=10.0m−1, σ=0, and m×m=21×21. (a) 110.00 °C, (b) 90.00 °C, (c) 150.00 °C, and (d) 60.00 °C.

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Figure 7

Iteration process of geometry and temperature identification for the case considered in Fig. 6(TH,ex=60.00°C)

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Figure 8

Variation of objective function and temperature of heating elements for the case considered in Fig. 6

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Figure 9

Several obtained candidate images for the case considered in Fig. 6

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Figure 10

Results of geometry and temperature identification for various shapes at h∕k=10.0m−1, σ=0, and m×m=21×21

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Figure 11

Effects of error in heat transfer coefficient on geometry and temperature identification for the case considered in Fig. 6. The exact heating element temperature TH,ex is fixed at 150.00 °C.

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Figure 12

Effects of temperature measurement uncertainty on geometry and temperature identification for the case considered in Fig. 6. The exact heating element temperature TH,ex is fixed at 90.00 °C.

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Figure 13

Effects of height of rectangular package on geometry and temperature identification for the case considered in Fig. 6. The exact heating element temperature TH,ex is fixed at 90.00 °C and temperature measurement uncertainty is at σ=1.0.

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Figure 14

Geometry and temperature identifications under various numbers of measurement points for the case with one heating element at h∕k=10.0m−1 and σ=0. The exact heating element temperature is fixed at 110.00 °C.

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Figure 15

Geometry and temperature identification using various grid systems for the cases with a triangular heating element at h∕k=10.0m−1 and σ=0. The exact temperature of heating element TH,ex is fixed at 100.00 °C.

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